Consider a contract V to deliver the maximal asset M * at time T in the situation when r = 0. We...

Consider a
contract V to deliver the maximal asset M∗ at
time T in the situation when r = 0. We have seen that its u Y price is given
by (6.7). (a) Determine the u S price of the contract V . Hint: Use
perspective mapping from (6.27). Note that the price function u S depends only
on one spatial variable y. (b) Show that the u S function satisfies the partial
differential (6.45) in the reduced form (r = 0). Verify the boundary
conditions, and determine the hedge using the function u S. Check that the
hedging portfolio agrees with the previously obtained representation in (6.8)
and (6.9). (c) Do the same analysis for the price u ∗ of the
contract V .